Question

Does the equation sin2(x) – 4 = 0 have any solutions? Explain.

Answer 1

No, the given equation:

`\sin^2x-4=0`

does not have any solution.

Explanation:

`sin^2x-4=0\\\\this\ means\ that\\\\(sinx-2)(sinx+2)=0\\\\so\ either\ sinx-2=0 or\ sinx+2=0\\\\i.e. sinx=2 or\ sinx=-2\\\\but\ this\ is\ not\ true\ as\ value\ of\ sinx\ lies\ between\ -1\ and\ 1`

Hence, the given equation:

`\sin^2x-4=0` does not have any solution.

Answer 2

Isolate sin(x) by adding 4 and taking the square root of both sides.
State that sin(x) = 2 or sin(x) = –2.State that –2 and 2 are undefined values of the inverse sine function.There are no solutions because –2 and 2 are not in the domain of the function.